Backward error analysis of the shift-and-invert Arnoldi algorithm
From MaRDI portal
Publication:303651
DOI10.1007/s00211-015-0759-9zbMath1350.65035OpenAlexW2192555061WikidataQ42243585 ScholiaQ42243585MaRDI QIDQ303651
Leo Taslaman, Christian Schröder
Publication date: 22 August 2016
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00211-015-0759-9
QR factorizationbackward error analysisorthonormalizationKrylov subspaceHessenberg matrixshift-and-invert Arnoldi algorithm
Computational methods for sparse matrices (65F50) Roundoff error (65G50) Orthogonalization in numerical linear algebra (65F25)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- A note on the error analysis of classical Gram-Schmidt
- Numerical stability of GMRES
- Roundoff error analysis of algorithms based on Krylov subspace methods
- The influence of orthogonality on the Arnoldi method
- Probabilistic upper bounds for the matrix two-norm
- Condition numbers and equilibration of matrices
- A Krylov--Schur Algorithm for Large Eigenproblems
- Improved Error Bounds for Inner Products in Floating-Point Arithmetic
- Error bounds on complex floating-point multiplication
- Structured Mapping Problems for Matrices Associated with Scalar Products. Part I: Lie and Jordan Algebras
- Stopping Criteria for Iterative Solvers
- Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
- ARPACK Users' Guide
- Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
- Accuracy and Stability of Numerical Algorithms
- The Matrix Eigenvalue Problem
- Convergence in Backward Error of Relaxed GMRES
- On the Compatibility of a Given Solution With the Data of a Linear System
- Solving linear least squares problems by Gram-Schmidt orthogonalization
- Round off error analysis for Gram-Schmidt method and solution of linear least squares problems
- The principle of minimized iterations in the solution of the matrix eigenvalue problem